The reality is that the universe is collectively made up of exactly the same bricks and mortar found in the periodic table of the chemical elements. We spectroscopically see these elements forged in stellar
nucleosynthesis in all corners of space. Something like unobtanium would have been cooked-up in supernovae and scattered across the galaxy.
Even if such a crystal existed - perhaps only forged under tremendous pressures deep inside a super-Earth - it would not be extractable. Even if it was, the chemistry would be easier to synthesize on Earth rather than building an interstellar Exxon Valdez to haul it between stars. Freight costs alone would kill any possibility of this material being commercially viable.
Finally, our scientists would always have the upper hand in such a discovery simply because Pandorans don't vote for Congressmen. A moon like this would be just an astrobiology curiosity. No private corporation would have the resources to mount an interstellar gold rush. What's more, corporations would be restricted by the Outer Space Treaty that explicitly forbids any government from claiming a celestial resource.
Floating Mountains – There are floating, superconducting magnetic mountains made of chunks of unobtanium on Pandora. On such a moon you might expect to find a huge electrical current inside a cylinder of a highly concentrated magnetic flux that is connected to the parent planet. Such a flux tube flowing between Jupiter and Io has the power output of about 2 trillion watts. But I'd stay clear of a field supposedly strong enough to lift a mountain. Living cells can be destroyed by extremely intense magnetic fields. The moon would have incredibly spectacular aurorae every night due to the magnetic field the moon must have to shield it from the intense radiation from the gas giant's magnetosphere. [This appears in the film, as some readers have pointed out, but I apparently missed it -- blinded by all the bioluminescence!]
"Do You Interface?" – The moon Pandora is the Gaia hypothesis gone wild. All living organisms - both animal and vegetable - intercommunicate. This Garden of Eden symbiosis seems inspired by the children's book series "Dinotopia." The Pandoran life forms even have a biological "plug ‘n play" capability. It's not clear how this would be an evolutionary advantage. It could just make dating complicated: "I've got a headache tonight dear, let's just interface."
Smurfs on Steroids – Given the infinite pathways evolution offers, it is very unlikely that 10-foot high blue humanoids would evolve elsewhere in the universe. You'd have to invoke a common origin such as panspermia from a mother super-race that seeded the galaxy with similar DNA. But clearly you can't show much of a love story between two blue blobs.
These science shortcomings aside; Avatar is still a powerfully engaging and memorable film. It's a long-awaited break from much less imaginative and silly story lines in most contemporary sci-fi films.
Artwork credit: Kees Veenenbos, Jon Spencer